01Overview - PubH8452 Longitudinal Data Analysis - Fall...

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PubH8452 Longitudinal Data Analysis - Fall 2011 Introduction Outline 1. Introduction: longitudinal studies, advantage and challenge. 2. Exploratory data analysis (EDA) and summary statistics. 3. Methods based on (general) linear models, for continuous outcomes. Weighted least-square (WLS). Maximum likelihood (ML) and restricted maximum likelihood (REML). Linear mixed models (LMM). 4. Methods based on generalized linear models, for binary, count and categorical outcomes. Generalized linear model (GLM), quasi-likelihood (QL). Generalized estimating equations (GEE). Generalized linear mixed models (GLMM). Transition models. 5. Special topics: Time-dependent covariates and causal inference. Missing data. Sample size considerations. 1
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PubH8452 Longitudinal Data Analysis - Fall 2011 Introduction Introduction Longitudinal study In a longitudinal study, each subject is measured multiple times, often over a considerable time interval, as opposed to cross-sectional data, where a single outcome is measured for each individual. Examples 1. Orthodontic measurements 2. Multicenter AIDS Cohort Study (MACS). 3. Indonesian Children’s Health Study (ICHS). 4. Analgesic crossover trial. 5. Epileptic seizures. 2
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PubH8452 Longitudinal Data Analysis - Fall 2011 Introduction Data example 1: Orthodontic Measurements Orthodontic measurements were taken from 27 children (16 boys and 11 girls) every two years from age 8 to 14. Note that here the data are balanced , that is, the subjects were measured at the same times with no missing data. Unbalanced data (due to design or missing data) is more common in biomedical studies and introduces extra technical difficulties. The following table presents the data for 11 girls in the “wide” form, i.e., one subject per row, with multiple columns representing multiple measurements of the same variable. Alternatively the data can also be presented in the “long” form, that is one row for each time point at which one measurement is taken. 3
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PubH8452 Longitudinal Data Analysis - Fall 2011 Introduction Table 1: Orthodontic measurements over time for 11 girls. P P P P P P P P P P P P PP Subject Age 8 10 12 14 01 21.0 20.0 21.5 23.0 02 21.0 21.5 24.0 25.5 03 20.5 24.0 24.5 26.0 04 23.5 24.5 25.0 26.5 05 21.5 23.0 22.5 23.5 06 20.0 21.0 21.0 22.5 07 21.5 22.5 23.0 25.0 08 23.0 23.0 23.5 24.0 09 20.0 21.0 22.0 21.5 10 16.5 19.0 19.0 19.5 11 24.5 25.0 28.0 28.0 4
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Introduction Data example 2: MACS: CD4+ Cell Number HIV attacks CD4+ cell which regulates the body’s immuno-response to infectious agents; An unin- fected individual has around 1100 cells per milliliter of blood. -2
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01Overview - PubH8452 Longitudinal Data Analysis - Fall...

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